|
I'll be here to observe and discuss the computational/game theoretic aspects of rock-paper-scissors.
|
#
¿
Feb 11, 2017 16:47
|
|
|
|
| # ¿ May 2, 2024 08:03 |
|
|
Covski posted:RPS and prisoner's dilemma are two very different beasts however, primarily since PD (at least with the classic values) is mathematically solvable, as well as cooperative rather than competitive assuming several rounds are played. This needs some clarification. Exactly how the iterated prisoner's dilemma goes down depends on whether the number of rounds is known ahead of time. If it is, then the rational thing to do (in the sense of maximizing expected utility) is to always defect. The game only gets more interesting if the number of rounds is unknown. I don't know in what sense the PD is solvable and RPS isn't. Can you explain a bit more?
|
|
#
¿
Feb 12, 2017 16:48
|
|
|
What beats choosing among all three options uniformly at random?
|
|
#
¿
Feb 12, 2017 23:00
|
|
|
Any interest in a series of informative posts on game theory? I think I can put together something that gets a lot of the basic ideas across in terms of Rock-Paper-Scissors and some other simple games.
|
|
#
¿
Feb 13, 2017 00:26
|
|
|
https://www.youtube.com/watch?v=cLHXYLHMhKI https://www.youtube.com/watch?v=Jp8znvfYbow https://www.youtube.com/watch?v=ncjcjpQzceQ Some game theory to come soon.
|
|
#
¿
Feb 14, 2017 01:24
|
|
|
Let's talk a little bit about game theory in general. What is game theory? The term "game theory" is a bit of a misnomer, as it doesn't really have anything to do with what we normally think of as games. The sort of situations that game theory deals with are scenarios where there are multiple people who do something, and the results that everyone gets depend on the actions that everyone took. People are out to maximize their own payoff, so they're going to try to pick the best move with the knowledge that everyone else is trying to pick their own best move. This is a simple idea at a high level, but it's powerful enough to model a very wide range of human activity. Can you give some examples? Sure. For this writeup, I'm going to limit the discussion to what are known as two-player simultaneous move games. Those are pretty much exactly what you'd expect: two people pick an action without knowing what the other person is doing, and they get a payoff that depends on both actions. I'm also going to assume that each player chooses from a finite set of moves, because that's a lot easier to describe than the more general case. The classic example of a game is the prisoner's dilemma. Wikipedia has a perfectly good description, so let me just quote it: quote:Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is: Betray/ Betray: -2, -2 Betray/Cooperate: 0, -3 Cooperate/Betray: -3, 0 Cooperate/Cooperate: -1, -1 Here the first column should be read as A's action/B's action, and the second column is A's payoff/B's payoff. Another classic example is the game of chicken: quote:The game of chicken models two drivers, both headed for a single-lane bridge from opposite directions. The first to swerve away yields the bridge to the other. If neither player swerves, the result is a costly deadlock in the middle of the bridge, or a potentially fatal head-on collision. It is presumed that the best thing for each driver is to stay straight while the other swerves (since the other is the "chicken" while a crash is avoided). Additionally, a crash is presumed to be the worst outcome for both players. This yields a situation where each player, in attempting to secure his best outcome, risks the worst. Swerve/Swerve: 0/0 Swerve/Straight: -1/1 Straight/Swerve: 1/-1 Straight/Straight: -10/-10 Finally, there's the topic of this thread, rock-paper-scissors. I don't need to describe that, but let me write out the payoff matrix just for completeness: Paper/Paper: 0/0 Paper/Rock: 1/-1 Paper/Scissors: -1/1 Rock/Paper: -1/1 Rock/Rock: 0/0 Rock/Scissors: 1/-1 Scissors/Paper: 1/-1 Scissors/Rock: -1/1 Scissors/Scissors: 0/0 In the interests of discussion, suppose that you're playing one of these games. You want to maximize your payoff, and you know that everyone else is trying to maximize their own payoff. What do you do? (Of course, you could just click on the Wikipedia links I gave and read the analysis there. But that'd be lame, so don't do it.)
|
|
#
¿
Feb 18, 2017 18:44
|
|
|
|
| # ¿ May 2, 2024 08:03 |
|
|
Fedule posted:Honestly I think there could be a good case for doing a classical game-theory-game megathread with continual game theory asides. Go all into the maths behind it and let people play nifty decision games. I'd be interested, but I think you'd have to treat this very carefully. The number of people who are willing to wade through all the math is vanishingly small compared to the number of people who would be interested in a more intuitive discussion.
|
|
#
¿
Mar 11, 2017 01:44
|
|